Important Definitions Regarding Parabola

Focus

The fixed point used to draw the parabola is called the focus (F). The focus is F(a, 0).

Directrix

The fixed line used to draw a parabola is called the directrix of the parabola. The equation of the directrix is x = −a.

Axis

The axis of the parabola is the axis of symmetry. The curve y² = 4ax is symmetrical about x-axis and hence x-axis or y = 0 is the axis of the parabola.

The axis of the parabola passes through the focus and perpendicular to the directrix.

Vertex

The point of intersection of the parabola and its axis is called its vertex. The vertex is V(0, 0).

Focal Distance

The focal distance is the distance between a point on the parabola and its focus.

Focal Chord

A chord which passes through the focus of the parabola is called the focal chord of the parabola.

Latus Rectum

It is a focal chord perpendicular to the axis of the parabola. The equation of the latus rectum is x = a.

End points of latus rectum and length of latus rectum

To find the end points, solve the equation of latus rectum x = a and y² = 4ax.

y = ±2a

The length of latus rectum = 4a